A small business invests 33,000 in equipment to produce a product. Each unit of the product costs $1.70 to produce and is sold for $5.00. How many items must be sold before the business breaks even?
number of units sold --- x
profit = 5x - 1.7x = 3.3x
3.3x = 33000
x = 33000/3.3 = 10000
cost = 33,000 + 1.70 n
revenue = 5 n
profit = 5 n - (33,000+1.7n)
so for zero profit
33,000 + 1.7 n = 5 n
33,000 = 3.3 n
n = 10,000
To find out how many items must be sold before the business breaks even, we need to calculate the breakeven point. The breakeven point is the quantity of items that must be sold in order to cover the total costs and start making a profit.
First, let's identify the total costs of the business. The small business invested $33,000 in equipment, which is a fixed cost. This cost does not change regardless of the number of items produced. Therefore, the total fixed cost is $33,000.
Next, determine the variable cost per unit. Each unit of the product costs $1.70 to produce.
To calculate the total variable costs, multiply the variable cost per unit by the quantity of items produced.
Total variable costs = Variable cost per unit * Quantity of items produced
Since we want to find the breakeven point, the total variable costs should equal the total fixed costs.
Total variable costs = Total fixed costs
Now we can set up the equation and solve for the quantity of items produced.
Variable cost per unit * Quantity of items produced = Total fixed costs
$1.70 * Quantity of items produced = $33,000
Quantity of items produced = $33,000 / $1.70
Finally, calculate the quantity of items that must be sold before the business breaks even:
Quantity of items produced = 33,000 / 1.70 = 19,411.76
The business needs to sell approximately 19,412 items before breaking even. Since you cannot sell a fraction of an item, rounding up to the nearest whole number gives the final answer.
Therefore, the business needs to sell at least 19,412 items before breaking even.